where \({u}\)  is the velocity, \(p\)  the pressure, and \(Re\)  the Reynolds number.
We consider the NSE posed on a bounded spatial domain in either \(\mathbb {R}^2\)  or \(\mathbb {R}^3\) , and supplemented with homogeneous Dirichlet boundary conditions and an appropriate initial condition.
The NSE (REF )–() can be cast in the general form (REF ) by choosing \({f}({u}) = Re^{-1} \Delta {u}- {u}\cdot \nabla {u}\)  (after applying the Leray projection, which maps the vector field into the divergence-free subspace of the underlying state space) [1]}.
